“…The most important route of transmission in gyrodactylids is direct contact between infected and uninfected fish, either between live hosts or from a dead to a live host (Scott and Anderson, 1984). Then, according to the simple transmission function d I /d t = βSI /( S + I ), where β is the transmission coefficient (Getz and Pickering, 1983; Anderson and May, 1992; Lloyd-Smith et al ., 2005 a , 2005 b ), S , the number of susceptible hosts, and I as the number of infected hosts (Smith et al ., 2009; McCallum et al ., 2017), the probability of transmission in the genus Gyrodactylus could be at a rate βSI (frequency-dependent transmission) rather than βSI /N (density-dependent transmission) (Heggberget and Johnsen, 1982; Johnsen and Jensen, 1986, 1992; Johnson et al ., 2011; Zhou et al ., 2017). Still, because pathogen transmission often occurs through more than one route, each of which may have a different functional relationship with population density (Ryder et al ., 2007), it is likely that Gyrodactylus transmission combines frequency- and density-dependent dynamics.…”